A fourth-order degenerate parabolic equation describing thin viscous flows over an inclined plane
type: Item
instance of: scholarly article
title: A fourth-order degenerate parabolic equation describing thin viscous flows over an inclined plane
zbMATH Open document ID: 0964.35084
DOI: 10.1016/S0893-9659(99)00130-5
author: Lorenzo Giacomelli
published in: Applied Mathematics Letters
publication date: 2001-07-02T00:00:00Z
review text: The author proves existence of nonnegative weak solutions for the fourth-order nonlinear degenerate parabolic equation \[ u_t+[u^n(b-cu_x+u_{xxx})]_x=0 \] which arises in the description of thin viscous flows over an inclined plane. Regularity, positivity and large-time behavior of these solutions are discussed as well.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K30
Mathematics Subject Classification ID: 76A05
zbMATH DE Number: 1428537
zbMATH Keywords: existence of nonnegative weak solutions
zbMATH Keywords: thin films
zbMATH Keywords: regularity, positivity and large-time behavior
MaRDI profile type: Publication
cites work: Spreading and instability of a viscous fluid sheet
cites work: Thin static drops with a free attachment boundary
cites work: On a Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions
cites work: Q5571843
cites work: Higher order nonlinear degenerate parabolic equations
cites work: Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
description: scientific article; zbMATH DE number 1428537